Question

Find the value of a , if the distance between points $P(a,-8,4)$ and $Q(-3,-5,4)$ is 5.

Answer 1

Given that

$P(x_1,y_1,z_1)=(a,-8,4)$

$Q(x_2,y_2,z_2)=(-3,-5,4)$

And distance $PQ=d=5$

Then, we know that,

Distance of

$PQ=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2+{(z_1-z_2)}^2}$

$PQ=\sqrt{{(a+3)}^2+{(-8+5)}^2+{(4-4)}^2}$

$5=\sqrt{{(a+3)}^2+{(-3)}^2}$

Squaring both side and we get,

$25={(a+3)}^2+9$

$25-9={(a+3)}^2$

${(a+3)}^2=16$

$a+3=4$

$a=4-3$

$a=1$